论文标题
仿射代数组的扭曲，II
Twisting of affine algebraic groups, II
论文作者
论文摘要
我们使用\ cite {g}来研究扭曲的cotriangular hopf代数$ {} _ j \ mathcal {o}（g）_ {j} $的代数结构，其中$ j $是hopf $ 2 $ - cocycle的nilpotent nilpotent nilpotent algebraic $ g $ g $ g $ cocycle $ g $ c $ c $ c $ c \ bey c $ cy cy cyver $ cy cy cy cy c $ cy cy cy cy cy cy cyver $ {c。特别是，我们表明$ {} _ j \ mathcal {o}（g）_ {j} $是一个具有Gelfand-kirillov dimension $ \ dim（g）$的现代noetherian域名$ {} _ j \ Mathcal {o}（g）_ {j} \ cong u（\ g）$作为代数，其中$ \ g = {\ rm lie}（g）$。我们还通过分析$（h，h）$ - 支持$ h \ subset $ j $ j $ $ j $ j $的双重coset的扭曲函数代数来确定$ {} _ j \ mathcal {o}（g）_ {j} $的有限尺寸不可减至表示。最后，我们制定了几个示例来说明我们的结果。
We use \cite{G} to study the algebra structure of twisted cotriangular Hopf algebras ${}_J\mathcal{O}(G)_{J}$, where $J$ is a Hopf $2$-cocycle for a connected nilpotent algebraic group $G$ over $\mathbb{C}$. In particular, we show that ${}_J\mathcal{O}(G)_{J}$ is an affine Noetherian domain with Gelfand-Kirillov dimension $\dim(G)$, and that if $G$ is unipotent and $J$ is supported on $G$, then ${}_J\mathcal{O}(G)_{J}\cong U(\g)$ as algebras, where $\g={\rm Lie}(G)$. We also determine the finite dimensional irreducible representations of ${}_J\mathcal{O}(G)_{J}$, by analyzing twisted function algebras on $(H,H)$-double cosets of the support $H\subset G$ of $J$. Finally, we work out several examples to illustrate our results.
